University of Warwick, Department of Sociology, 2012/13 SO 201: SSAASS (Surveys and Statistics) (Richard Lampard) Measuring association and inequality (Week 18)

Did social mobility increase or decrease in England and Wales during the 20th Century? ‘Classic’ finding based on 1972 Oxford Mobility Study (Goldthorpe et al. 1987): Constant ‘social fluidity’, i.e. no change in association once changes in the occupational structure (which allowed increased upwards mobility) had been taken into account. But this finding relies on the use of odds ratios as a measure of association, and arguably equates this form of association with ‘inequality’...

The data... Derived from Goldthorpe et al. (1987: 71 [Table 3.1])

The measures... Differences in ‘Service class’ attainment: 59.0% - 20.0% = 39.0%; 64.7% – 23.1% = 41.6% 41.6 / 39.0 = 1.067, i.e. a 6.7% increase. Cramér’s V = 0.296 and 0.329 0.329 / 0.296 = 1.111, i.e. an 11.1% increase Odds ratios = 5.752 and 6.107 6.107 / 5.752 = 1.062, i.e. a 6.2% increase (LR chi-square for difference within a log-linear model = 0.177 on 1 d.f.; p = 0.674 > 0.05)

... and more measures Gini coefficients = 0.169 and 0.183 0.183 / 0.169 = 1.083, i.e. an 8.3% increase. Tog coefficients = 0.329 and 0.375 0.375 / 0.329 = 1.140, i.e. a 14.0% increase z = 2.19; p = 0.029 < 0.05 [N.B. Based on a more detailed, 4 x 4 cross-tabulation; see Lampard (2000: 10).]

What is the Gini coefficient? Originally a measure of income inequality: see Marsh and Elliott (2009) or Marsh (2008) ... But can be adapted to measure other forms of inequality and segregation (see Le Grand and Rabin, 1986; Lampard, 1994). ... including inequality in educational attainment according to class background (Hellevik, 1997).

More data... Hellevik (1997: 391 [Table 2]) re-presents data from a paper by Heath and Clifford (1990) on educational attainment (‘O’-levels) according to class background: % differences in attaining ‘O’-levels or higher between Classes I-II and Classes VI-VII: Birth cohorts - 1930-39: 40%; 1940-49: 40%; 1950-59: 42%; 1960-69: 33%. Heath, A.F. and Clifford, P. 1990. ‘Class inequalities in education in the twentieth century’, Journal of the Royal Statistical Society (Series A) 153: 1-16. Class 1930-39 1940-49 1950-59 1960-69 I – II 58% 67% 84% 87% III – V 31% 46% 74% VI - VII 18% 27% 42% 54%

Other measures... Comparing I – II, III –V and VI –VII: Lambda - 1930-39: 0.46; 1940-49: 0.43; 1950-59: 0.49; 1960-69: 0.42. Cramér’s V - 1930-39: 0.32; 1940-49: 0.31; 1950-59: 0.33; 1960-69: 0.31. Comparing I – II and VI –VII: Odds ratios: 1930-39: 6.29; 1940-49: 5.49; 1950-59: 7.25; 1960-69: 5.70.

But... Gini coefficient (comparing I – II, III –V and VI –VII): 1930-39: 0.25 1940-49: 0.20 1950-59: 0.15 1960-69: 0.11

Debates! In addition to Goldthorpe et al. (1987), authors such as Marshall and Swift (1999) see the removal of the impact of changes in the distributions of origins and outcomes as a necessary step to assessing underlying change. However, authors such as Saunders (1997), Hellevik (2002) and Ringen (2006) are not convinced that odds ratios retain all the aspects of the changing patterns of social mobility and/or educational attainment that are relevant...